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A set of two or more inequalities.

A set of two or more equations.

Let $a$ and $b$ be real numbers, variables, or algebraic expressions.
1. \({\rm{ }}{a^3} + {b^3} = \left( {a + b} \right)\left( {{a^2} – ab + {b^2}} \right)\) 2. \({\rm{ }}{a^3} – {b^3} = \left( {a – b} \right)\left( {{a^2} + ab + {b^2}} \right)\)

Let $a$ and $b$ be real numbers, variables, or algebraic expressions.
\(\left( {a + b} \right)\left( {a – b} \right) = {a^2} – {b^2}\)

The result when two or more numbers are added.

Add the opposite of the integer being subtracted to the other integer.

Rewrite the fractions so that they have like denominators. Then use the rule for subtracting fractions with like denominators.

Let $a$, $b$, and $c$ be integers with $c$\( \ne \)0. Then use the following rule: \(\frac{a}{c} – \frac{b}{c} = \frac{{a – b}}{c}\).

Subtract the same quantity form each side. If \(a < b\) , then \(a + c < b + c\).

Let \({a_n},{\rm{ }}{a_{n – 1}},{\rm{ }}…,{\rm{ }}{a_2},{\rm{ }}{a_1},{\rm{ }}{a_0}\) be real numbers and let n be a non negative number. Order the terms with descending exponents.

\[{a_n}{x^n} + {a_{n – 1}}{x^{n – 1}} + … + {a_2}{x^2} + {a_1}x + {a_0}\]

Let \({a_n},{\rm{ }}{a_{n – 1}},{\rm{ }}…,{\rm{ }}{a_2},{\rm{ }}{a_1},{\rm{ }}{a_0}\) be real numbers and let n be a nonnegative number. Order the terms with descending exponents.

\[{a_n}{x^n} + {a_{n – 1}}{x^{n – 1}} + … + {a_2}{x^2} + {a_1}x + {a_0} = 0\]

Let $a$ and $b$ be real numbers. \(a + bi\)

Let $a$ and $b$ be real numbers, variables, or algebraic expressions. If $a = b$, then it follows that $a^2 = b^2$.

The equation \({u^2} = d,{\rm{ }}d < 0\), has exactly two solutions: \(u = \sqrt {\left| d \right|} i\) and \(u = - \sqrt {\left| d \right|} i\). These solutions can also be written as \(u = \pm \sqrt {\left| d \right|} i\).

Let $u$ be a real number, a variable, or an algebraic expression, and let $d$ be a positive real number; then the equation $u^2 = d$ has exactly two solutions.
If $u^2 = d$, then \(u = \sqrt d \) and \(u = – \sqrt d \). These solutions can also be written as \(u = \pm \sqrt d \).

If $x$ is a real number, then \(\sqrt {{x^2}} = \left| x \right|\). For a special case in which you know that $x$ is a non-negative real number, you can write \(\sqrt {{x^2}} = x\).

When $n = 2$ in \(a = {b^n}\).

Let $a$ and $b$ be real numbers, variables, or algebraic expressions. \({\left( {a + b} \right)^2} = {a^2} + 2ab + {b^2}\) \({\left( {a – b} \right)^2} = {a^2} – 2ab + {b^2}\)

Finding all values of the variable(s) for which an inequality set is true.

Find all values of the variable(s) for which the equation is true.

The values of the variable(s) for which an equation is true.

The set of all real numbers that are solutions of an inequality.

The form of the equation \(y = mx + b\) where the slope of the line is $m$ and the $y$-intercept is \(\left( {0,b} \right)\).

The change in $y$ divided by the change in $x$ of two points.

Let $a$, $b$, and $c$ represent real numbers, variables, or algebraic expressions such that \(b \ne 0\) and \(c \ne 0\). Then the following is valid. \(\frac{{ac}}{{bc}} = \frac{a}{b}\).

A radical expression is said to be in simplest form when all three of the following statements are true. 1. All possible $n$th-powered factors have been removed from each radical. 2. No radical contains a fraction. 3. No denominator of a fraction contains a radical.

Remove symbols of grouping and combine like terms.

See quadratic equations.

Writing a number, usually very large or very small, in the form \(c \times {10^n}\), where \(1 \le c < 10\) and $n$ is an integer.

The solutions of an equation are said to satisfy the equation when the equation yields a true statement.